to say something without an intention of actually doing it. Making an offer that is not intended to be fulfilled or even taken up by someone.

Rocky: if theres anything you﻿ need let us know
Mom: actually there is something you could do for us
Rocky: really? wow no ones ever actually taken us up on our offer before
CeCe: yea havent you guys ever heard of an empty gesture?

Making a nice (fake) gesture for someone when you don't really mean it, hoping that the person who you are making that gesture to won't actually as you for a favor, or follow up on that offer you made. You just say it to seem like a nice person. This phrase is used in Curb Your Enthusiasm.

Larry David: Well, If there is anything I can do, let me know.
Marty Funkhouser: You know what, there is something you can do.
Larry David: What, are you kidding?
Marty Funkhouser: What, you didn't mean it?
Larry David: Of course not!
Marty Funkhouser: Well why did you say it then?
Larry David: You know, it's an empty gesture; something to say!
Larry David (saying to Jeff Greene): Don't make an empty gesture to a Funkhouser, they'll take you up on it!